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Chapter5_9 - PHY4604 R D Field Spectrum of Helium...

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PHY4604 R. D. Field Department of Physics Chapter5_9.doc University of Florida Helium (2) Ground State of Helium: The lowest energy occurs when n 1 = 1 and n 2 = 1 and hence eV eV E E E E E He 8 . 108 ) 6 . 13 ( 8 8 0 1 1 11 0 = + = = . The corresponding space part of the wave function is 0 2 1 / ) ( 2 3 0 2 100 1 100 2 1 11 2 1 0 8 ) ( ) ( ) , ( ) , ( r r r e r r r r r r r + = = = π ψ ψ ψ ψ r v r v r v and is symmetric under the interchange of the two electrons. Hence, the ground state of Helium must be in the “singlet” spin state χ S . True Ground State: The true ground state of Helium is indeed in the “singlet” spin state but the actual ground state energy is -79 eV (compared to the -109 eV we got by neglecting the electron repulsion). Excited States of Helium: The ionization energy is the energy required to remove one electron from the ground state to infinity as follows: eV E E E E E E He ionization 4 . 54 4 2 0 1 1 1 = = + = . Note that the onset of the continuum lies below the E 22 state ( i.e. n 1 = 2 and n 2 = 2).
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